Fgc: fighting game community. Games like Street Fighter, Tekken, etc.

Neutral: the point in the game where neither player has an advantage, like in the beginning where the players are just moving back and forth trying to get the first hit in, and thereby gain advantage.

Puppy girls: y'know, girls who wear puppy ears and collars or whatever.

Clicker training: a form of dog training that involves reinforcing good behavior with a little device that makes a click noise, which can help the dog more precisely understand what action was correct than rewarding with food after.

So I think what he's saying is that when you train a puppy girl with clicker training, you're basically training them to quickly react to click sounds, like how players might respond to the sound of their opponents controller as a way of predicting their moves. So they'd be very good at the neutral game, since they'd be able to get the first hit in or effectively block/counter the opponents first hit. The guy responding is suggesting that if he brought tennis balls he could throw them in the middle of the match and distract the puppy girl - since dogs chase tennis balls - thereby giving him the upper hand. I hope this helps lol

Edit: the part about clicker training